.TH CTRSM l "16 October 1992" "BLAS routine" "BLAS routine"
.SH NAME
CTRSM - solve one of the matrix equations   op( A )*X = alpha*B, or X*op( A ) = alpha*B,
.SH SYNOPSIS
.TP 17
SUBROUTINE CTRSM
( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
B, LDB )
.TP 17
.ti +4
CHARACTER*1
SIDE, UPLO, TRANSA, DIAG
.TP 17
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INTEGER
M, N, LDA, LDB
.TP 17
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COMPLEX
ALPHA
.TP 17
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COMPLEX
A( LDA, * ), B( LDB, * )
.SH PURPOSE
CTRSM  solves one of the matrix equations

where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

   op( A ) = A   or   op( A ) = A'   or   op( A ) = conjg( A' ).

The matrix X is overwritten on B.
.br

.SH PARAMETERS
.TP 7
SIDE   - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:

SIDE = 'L' or 'l'   op( A )*X = alpha*B.

SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

Unchanged on exit.
.TP 7
UPLO   - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:

UPLO = 'U' or 'u'   A is an upper triangular matrix.

UPLO = 'L' or 'l'   A is a lower triangular matrix.

Unchanged on exit.

TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:

TRANSA = 'N' or 'n'   op( A ) = A.

TRANSA = 'T' or 't'   op( A ) = A'.

TRANSA = 'C' or 'c'   op( A ) = conjg( A' ).

Unchanged on exit.
.TP 7
DIAG   - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:

DIAG = 'U' or 'u'   A is assumed to be unit triangular.

DIAG = 'N' or 'n'   A is not assumed to be unit
triangular.

Unchanged on exit.
.TP 7
M      - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
.TP 7
N      - INTEGER.
On entry, N specifies the number of columns of B.  N must be
at least zero.
Unchanged on exit.
.TP 7
ALPHA  - COMPLEX         .
On entry,  ALPHA specifies the scalar  alpha. When  alpha is
zero then  A is not referenced and  B need not be set before
entry.
Unchanged on exit.
.TP 7
A      - COMPLEX          array of DIMENSION ( LDA, k ), where k is m
when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
upper triangular part of the array  A must contain the upper
triangular matrix  and the strictly lower triangular part of
A is not referenced.
Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
lower triangular part of the array  A must contain the lower
triangular matrix  and the strictly upper triangular part of
A is not referenced.
Note that when  DIAG = 'U' or 'u',  the diagonal elements of
A  are not referenced either,  but are assumed to be  unity.
Unchanged on exit.
.TP 7
LDA    - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
.TP 7
B      - COMPLEX          array of DIMENSION ( LDB, n ).
Before entry,  the leading  m by n part of the array  B must
contain  the  right-hand  side  matrix  B,  and  on exit  is
overwritten by the solution matrix  X.
.TP 7
LDB    - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in  the  calling  (sub)  program.   LDB  must  be  at  least
max( 1, m ).
Unchanged on exit.

Level 3 Blas routine.

-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.

.. External Functions ..

.. External Subroutines ..

.. Intrinsic Functions ..

.. Local Scalars ..
